Chiral and trace anomalies in Deeply Virtual Compton Scattering

Abstract

Inspired by recent work by Tarasov and Venugopalan, we calculate the one-loop quark box diagrams relevant to polarized and unpolarized Deep Inelastic Scattering (DIS) by introducing off-forward momentum $l^{\mu }$ as an infrared regulator. In the polarized case, we rederive the pole $1/l^2$ related to the axial (chiral) anomaly. In addition, we obtain the usual logarithmic term and the DIS coefficient function. We interpret the result in terms of the generalized parton distributions (GPDs) $\tilde{H}$ and $\tilde{E}$ and discuss the possible violation of QCD factorization for the Compton scattering amplitude. Remarkably, we also find poles in the unpolarized case which are remnants of the trace anomaly. We argue that these poles are cancelled by the would-be massless glueball poles in the GPDs $H$ and $E$ as well as in their moments, the nucleon gravitational form factors $A,B$ and $D$. This mechanism sheds light on the connection between the gravitational form factors and the gluon condensate operator $F^{\mu \nu }{F}_{\mu \nu }$.

arXiv comment14 pages, 1 figure, minor additions to text, updated references, version to appear in PRD

References in corpus (25)

• Gauge-Invariant Decomposition of Nucleon Spin and Its Spin-Off
• Package-X: A Mathematica package for the analytic calculation of one-loop integrals
• A first unbiased global determination of polarized PDFs and their uncertainties
• Evidence for polarization of gluons in the proton
• Proof of Factorization for Deeply Virtual Compton Scattering in QCD
• One-Loop Corrections and All Order Factorization In Deeply Virtual Compton Scattering
• Predictions from conformal algebra for the deeply virtual Compton scattering
• The Trace Anomaly and Massless Scalar Degrees of Freedom in Gravity
• Diffractive photoproduction of $J/\psi$ and ${\rm Y}$ using holographic QCD: gravitational form factors and GPD of gluons in the proton
• Helicity-Flip Off-Foward Parton Distributions of the Nucleon
• Helicity skewed quark distributions of the nucleon and chiral symmetry
• Quark and gluon contributions to the QCD trace anomaly
• NLO Corrections to Deeply-Virtual Compton Scattering
• NLO corrections to timelike, spacelike and double deeply virtual Compton scattering
• Nucleon mass radii and distribution: Holographic QCD, Lattice QCD and GlueX data
• Deeply Virtual Compton Scattering to the twist-four accuracy: Impact of finite-$t$ and target mass corrections
• Nucleon D-term in holographic QCD
• How well do we know the gluon polarization in the proton?
• The role of the chiral anomaly in polarized deeply inelastic scattering I: Finding the triangle graph inside the box diagram in Bjorken and Regge asymptotics
• Anomaly Poles as Common Signatures of Chiral and Conformal Anomalies
• The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics
• Parton distribution function for the gluon condensate
• $CP$-odd gluonic operators in QCD spin physics
• Factorisation in Deeply Virtual Compton Scattering: Local OPE Formalism and Structure Functions
• Parton distribution function for topological charge at one loop

Cited by in corpus (5)

• Generalized parton distributions at zero skewness
• Small $x$ Physics Beyond Eikonal Approximation: an Effective Hamiltonian Approach
• Chiral and trace anomalies in Deeply Virtual Compton Scattering II: QCD factorization and beyond
• Generalized parton distributions from the pseudo-distribution approach on the lattice
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution